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Mathematical Treasure: Dedekind on the Nature of Number

Frank J. Swetz (The Pennsylvania State University)

Richard Dedekind (1831–1916) was a German mathematician and a student of Gauss. He is particularly remembered for his work on the foundations of the real numbers. Dedekind developed a major redefinition of rational numbers in terms of arithmetic concepts. In this Carus publication of 1909, Essays on the Theory of Number, we find the first English translation of two of his classical mathematics lectures: Stetigkeit und Irrationale Zahlen (1872) and Was sind und was sollen die Zahlen? (1888).

Here on pages 12 and 13 of the Essays, we find a discussion of the Dedekind Cut used to define an irrational number.

The Special Collections staff at the Linderman Library of Lehigh University in Bethlehem, Pennsylvania, is pleased to cooperate with the Mathematical Association of America to exhibit this and other items from the Library’s holdings in Mathematical Treasures. In particular, Convergence would like to thank Lois Fischer Black, Curator, Special Collections, and Ilhan Citak, Archives and Special Collections Librarian, for their kind assistance in helping to make this display possible. You may use these images in your classroom; all other uses require permission from the Special Collections staff, Linderman Library, Lehigh University.

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Dedekind on the Nature of Number," Convergence (June 2014)